Noise coupling in mixed-signal systems from shared power distribution networks can be a critical problem. The concept of power filtering in high-speed digital systems as introduced in this thesis is as fundamental as signal filtering in high-frequency analog systems. Sensitive RF ICs have to be isolated from voltage fluctuations caused by simultaneously switching digital drivers. Suppressing this noise is therefore critical to the performance of mixed-signal systems. Conventional approaches, such as decoupling capacitors, do not work at microwave frequencies due to the parasitic effects of the components. Existing methodologies for microwave power filtering are design intensive or narrow-band solutions. This thesis introduces the concept of the power archipelago, a new methodology for minimizing the transfer impedance of the power distribution network, as well as several design considerations. The power archipelago is essentially a lumped element microwave filter in which the discrete elements have been translated to embedded elements, effectively filtering out noise from the power distribution network. The power archipelago design methodology, based on microwave design theory, for the first time provides systematic design methodology for power filtering. Hardware measurements on passive test boards show good isolation across a wide frequency band.